Question 1193299
.



            Here is the way to solve the problem  MENTALLY.



<pre>
Take your original equation

    w*(2w+1) = 15


and multiply both sides by 2.  You will get an EQUIVALENT equation

    2w*(2w+1) = 30.
    

Now ask yourself, which two consecutive numbers, 2w and 2w+1 make the product of 30.


One guess is obvious: the numbers are 5 and 6.
Hence, 2w = 5,  which gives  w = 5/2 = 2.5.


    Another guess  is -5 and -6, 
    which gives  2w+1 = -5,   2w = -6,   w = -3.
</pre>

Solved.